Generalized Bandit Regret Minimizer Framework in Imperfect Information Extensive-Form Game

• URL: http://arxiv.org/abs/2203.05920v4
• Date: Fri, 18 Aug 2023 14:16:12 GMT
• Title: Generalized Bandit Regret Minimizer Framework in Imperfect Information Extensive-Form Game
• Authors: Linjian Meng, Yang Gao
• Abstract summary: We consider the problem in the interactive bandit-feedback setting where we don't know the dynamics of the IIEG. To learn NE, the regret minimizer is required to estimate the full-feedback loss gradient $ellt$ by $v(zt)$ and minimize the regret. We present a novel method SIX-OMD to learn approximate NE. It is model-free and extremely improves the best existing convergence rate from the order of $O(sqrtX B/T+sqrtY C/T)$ to $O(
• Score: 9.933208900617174
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Regret minimization methods are a powerful tool for learning approximate Nash equilibrium (NE) in two-player zero-sum imperfect information extensive-form games (IIEGs). We consider the problem in the interactive bandit-feedback setting where we don't know the dynamics of the IIEG. In general, only the interactive trajectory and the reached terminal node value $v(z^t)$ are revealed. To learn NE, the regret minimizer is required to estimate the full-feedback loss gradient $\ell^t$ by $v(z^t)$ and minimize the regret. In this paper, we propose a generalized framework for this learning setting. It presents a theoretical framework for the design and the modular analysis of the bandit regret minimization methods. We demonstrate that the most recent bandit regret minimization methods can be analyzed as a particular case of our framework. Following this framework, we describe a novel method SIX-OMD to learn approximate NE. It is model-free and extremely improves the best existing convergence rate from the order of $O(\sqrt{X B/T}+\sqrt{Y C/T})$ to $O(\sqrt{ M_{\mathcal{X}}/T} +\sqrt{ M_{\mathcal{Y}}/T})$. Moreover, SIX-OMD is computationally efficient as it needs to perform the current strategy and average strategy updates only along the sampled trajectory.

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